The invention relates to a position determination method for points to be surveyed, comprising a geodetic device.
A multiplicity of measuring methods have been known since antiquity for recording properties of defined points in a measuring environment, in particular of data with spatial reference. The location of a measuring device in addition to any reference points present and direction, distance and angle to measuring points are recorded as standard spatial data. While in many applications the position of the geodetic measuring device is known and unknown positions are measured, there are, however, also applications in which some measuring points are known or are surveyed and hence serve as reference points but the location of the surveying device is unknown.
A generally known example of such surveying devices or geodetic devices is the theodolite or a total station. An overview of geodetic measuring apparatuses of the prior art appears in “Elektronische Entfernungs- und Richtungsmessung [Electronic distance and direction measurement]” by R. Joeckel and M. Stober, 4th edition, Verlag Konrad Wittwer, Stuttgart 1999. Such devices have angle and distance measuring functions which permit a direction and distance determination to a selected target. The angle or distance magnitudes are determined in the internal reference system of the device and, if appropriate, have to be linked to an external reference system for an absolute position determination.
In principle, the position of the geodetic device itself, i.e. the station coordinates of the measuring device, or the position of new points to be surveyed as so-called free stationing, can be derived from measurements to known, fixed measuring points as reference points. This process is also designated as referencing of the measuring device position or of the new points relative to the measured reference points of known position.
For this purpose, the position of the known reference points relative to the stand point in a local coordinate system is first calculated. With the aid of the known coordinates of these reference points, if more than the necessary number of measurements are present, matched transformation parameters are calculated, from which the sought station coordinates or the sought coordinates of the new points can then be derived. The process can be illustrated by an example: distances and directions are measured to some surrounding points and the position of these points relative to the location, i.e. in a local coordinate system, is plotted on a transparent sheet. A map of the desired coordinate system is now placed underneath this sheet. This system may be the national coordinate system or the coordinate system of a specific construction product. Measured reference points are now also to be found on this map. The sheet is rotated and shifted until the sheet points agree as well as possible with the points drawn on the map, which can be effected algorithmically by fit calculation according to the least squares method. Thereafter, the position of the geodetic measuring device and the positions of the new points measured in relative terms can be read on the map. This principle is applied not graphically but analytically, it always being necessary for the point number of a measuring point and the measured values from the geodetic device to this measuring point to be known and assigned.
The software for the calculations required for this purpose is integrated into most modern total stations or tacheometers. However, this still means that measurement of all reference points and derivation of a transformation relationship between device-related and absolute coordinate system must first be effected and only thereafter is it possible to start the measurement of new points actually to be surveyed. The minimum number of initially measured reference points which is required for such referencing is dependent on the surveying situation and on the relative measured quantities registered during the measurement, for example distance and direction from the geodetic device to the reference points. In practice, however, measurements over and above this to further known reference points are carried out where possible in order to obtain data on the reliability of the results, i.e. coefficient of determination, by agreement.
Algorithms by means of which overdetermined referencing of new points—for example referencing relative to more than two measured fixed points—is effected may be, for example, similarity transformations in combination with an averaging fit which is also referred to in the technical literature as Helmert transformation.
The erection of a total station and the determination of the actual station coordinates from known measuring points are generally tailored to the trained surveying engineer with regard to user guidance. The user must reliably identify in the field the reference points used for calculating the station coordinates and must assign to said reference points the correct point numbers which produce the linkage to the position of the reference point. After all known reference points were surveyed, the fitted relationship can then be derived and hence the absolute device position determined—i.e. the geodetic device referenced with respect to the reference points. Only thereafter is it possible to start measurement and surveying of the new points actually to be surveyed, the absolute positions of new points being determined in each case on the basis of the determined absolute device position from relative quantities of new points measured thereby.
Position determination methods of the prior art are therefore based on the surveying of known reference points whose measured values are recorded or further processed before the beginning of measurements to new points actually to be surveyed, in order to reference the subsequently measured new points relative to the reference points by derivation of a transformation relationship between device-related and absolute coordinate system. This necessary sequence with the prior stationing of the geodetic device by measurement of the known reference points, the derivation of the transformation relationship being carried out therefrom once, and the subsequent surveying of the new points proves to be complicated, slows down the method and increases the susceptibility to errors since there is a danger that reference points and new points will be confused or measured in duplicate. If, for example, a reference point and a new point have spatial directions similar from the location of the geodetic device, in position determination methods of the prior art a measurement of all reference points of the set of reference points must nevertheless first be effected, after which it is necessary to swivel back to the new point then to be surveyed.
In methods of the prior art, too, the relationship between absolute and device-related reference system is always derived once and this is then used for absolute position determination of the geodetic device and for transformation of measured values determined in all subsequent measurements of new points. If, for example in the measurement of the reference points from the set of reference points, effected for stationing of the device, a reference point is incorrectly read in or is forgotten and/or the transformation relationship is incorrectly derived, all measured values determined to the new points in the measuring process are also incorrectly transformed into the external reference system.